Physics-Based Animation

Antoine Chan-Lock, Jesús Pérez, Miguel A. Otaduy

We propose a novel formulation of elastic materials based on high-order interpolants, which fits accurately complex elastic behaviors, but remains conservative. The proposed high-order interpolants can be regarded as a high-dimensional extension of radial basis functions, and they allow the interpolation of derivatives of elastic energy, in particular stress and stiffness. Given the proposed parameterization of elasticity models, we devise an algorithm to find optimal model parameters based on training data. We have tested our methodology for the homogenization of 2D microstructures, and we show that it succeeds to match complex behaviors with high accuracy.

High-Order Elasticity Interpolants for Microstructure Simulation

D. Dorda, D. Peter, D. Borer, N.B. Huber, I. Sailer, M. Gross, B. Solenthaler, B. Thomaszewski

Algorithms at the intersection of computer graphics and medicine have recently gained renewed attention. A particular interest are methods for virtual surgery planning (VSP), where treatment parameters must be carefully chosen to achieve a desired treatment outcome. FEM simulators can verify the treatment parameters by comparing a predicted outcome to the desired one. However, estimating the optimal parameters amounts to solving a challenging inverse problem. In current clinical practice it is solved manually by surgeons, who rely on their experience and intuition to iteratively refine the parameters, verifying them with simulated predictions. We prototype a differentiable FEM simulator and explore how it can enhance and simplify treatment planning, which is ulti- mately necessary to integrate simulation-based VSP tools into a clinical workflow. Specifically, we define a parametric treatment model based on surgeon input, and with analytically derived simulation gradients we optimise it against an objective defined on the visible facial 3D surface. By using sensitivity analysis, we can rapidly explore the solution-space through first-order approximations, which allow the surgeon to interactively visualise the effect of parameter variations on a given treatment plan. The objective function allows landmarks to be freely chosen, accommodating the multiple methodologies in clinical planning. We show that even with a very sparse set of guiding landmarks, our simulator robustly converges to a feasible post-treatment shape.

Differentiable Simulation for Outcome-Driven Orthognathic Surgery Planning

Juan J. Casafranca, Miguel A. Otaduy

The simulation of complex deformation problems often requires enrichment techniques that introduce local high-resolution detail on a generally coarse discretization. The use cases include spatial or temporal refinement of the discretization, the simulation of composite materials with phenomena occurring at different scales, or even codimensional simulation. We present an efficient simulation enrichment method for both local refinement of the discretization and codimensional effects. We dub our method Voronoi filters, as it combines two key computational elements. One is the use of kinematic filters to constrain coarse and fine deformations, and thus provide enrichment functions that are complementary to the coarse deformation. The other one is the use of a centroidal Voronoi discretization for the design of the enrichment functions, which adds high-resolution detail in a compact manner while preserving the rigid modes of coarse deformation. We demonstrate our method on simulation examples of composite materials, hybrid triangle-based and yarn-level simulation of cloth, or enrichment of flesh simulation with high-resolution detail

Voronoi Filters for Simulation Enrichment

Zhang, Paul, Dmitriy Smirnov, Justin Solomon

Much of computer-generated animation is created by manipulating meshes with rigs. While this approach works well for animating articulated objects like animals, it has limited flexibility for animating less structured free-form objects. We introduce Wassersplines, a novel trajectory inference method for animating unstructured densities based on recent advances in continuous normalizing flows and optimal transport. The key idea is to train a neurally-parameterized velocity field that represents the motion between keyframes. Trajectories are then computed by advecting keyframes through the velocity field. We solve an additional Wasserstein barycenter interpolation problem to guarantee strict adherence to keyframes. Our tool can stylize trajectories through a variety of PDE-based regularizers to create different visual effects. We demonstrate our tool on various keyframe interpolation problems to produce temporally-coherent animations without meshing or rigging

Wassersplines for Neural Vector Field–Controlled Animation

Song Bai, Craig Schroeder

In this paper we analyze the stability of the explicit material point method (MPM). We focus on PIC, APIC, and CPIC transfers using quadratic and cubic splines in two and three dimensions. We perform a fully three-dimensional Von Neumann stability analysis to study the behavior within the bulk of a material. This reveals the relationship between the sound speed, CFL number, and actual time step restriction and its dependence on discretization options. We note that boundaries are generally less stable than the interior, with stable time steps generally decreasing until the limit when particles become isolated. We then analyze the stability of a single particle to derive a novel time step restriction that stabilizes simulations at their boundaries. Finally, we show that for explicit MPM with APIC or CPIC transfers, there are pathological cases where growth is observed at arbitrarily small time steps sizes. While these cases do not necessarily pose a problem for practical usage, they do suggest that a guarantee of stability may be theoretically impossible and that necessary but not sufficient time step restrictions may be a necessary and
practical compromise.

Stability Analysis of Explicit MPM

Zhongyun He, Jesús Pérez, Miguel A. Otaduy

Numerical coarsening methods offer an attractive methodology for fast simulation of objects with high-resolution heterogeneity. However, they rely heavily on preprocessing, and are not suitable when objects undergo dynamic material or topology updates. We present methods that largely accelerate the two main processes of numerical coarsening, namely training data generation and the optimization of coarsening shape functions, and as a result we manage to leverage runtime numerical coarsening under local material updates. To accelerate the generation of training data, we propose a domain-decomposition solver based on substructuring that leverages local factorizations. To accelerate the computation of coarsening shape functions, we propose a decoupled optimization of smoothness and data fitting. We evaluate quantitatively the accuracy and performance of our proposed methods, and we show that they achieve accuracy comparable to the baseline, albeit with speed-ups of orders of magnitude. We also demonstrate our methods on example simulations with local material and topology updates.

Fast Numerical Coarsening with Local Factorizations

Yongxu Jin , Yushan Han , Zhenglin Geng , Joseph Teran , Ronald Fedkiw

We present a novel paradigm for modeling certain types of dynamic simulation in real-time with the aid of neural networks. In order to significantly reduce the requirements on data (especially time-dependent data), as well as decrease generalization error, our approach utilizes a data-driven neural network only to capture quasistatic information (instead of dynamic or time-dependent information). Subsequently, we augment our quasistatic neural network (QNN) inference with a (real-time) dynamic simulation layer. Our key insight is that the dynamic modes lost when using a QNN approximation can be captured with a quite simple (and decoupled) zero-restlength spring model, which can be integrated analytically (as opposed to numerically) and thus has no time-step stability restrictions. Additionally, we demonstrate that the spring constitutive parameters can be robustly learned from a surprisingly small amount of dynamic simulation data. Although we illustrate the efficacy of our approach by considering soft-tissue dynamics on animated human bodies, the paradigm is extensible to many different simulation frameworks.

Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks

Amir Hossein Rabbani, Jean-Philippe Guertin , Damien Rioux-Lavoie, Arnaud Schoentgen, Kaitai Tong, Alexandre Sirois-Vigneux, Derek Nowrouzezahrai

Poisson equations appear in many graphics settings including, but not limited to, physics-based fluid simulation. Numerical solvers for such problems strike context-specific memory, performance, stability and accuracy trade-offs. We propose a new Poisson filter-based solver that balances between the strengths of spectral and iterative methods. We derive universal Poisson kernels for forward and inverse Poisson problems, leveraging careful adaptive filter truncation to localize their extent, all while maintaining stability and accuracy. Iterative composition of our compact filters improves solver iteration time by orders-of-magnitude compared to optimized linear methods. While motivated by spectral formulations, we overcome important limitations of spectral methods while retaining many of their desirable properties. We focus on the application of our method to high-performance and high-fidelity fluid simulation, but we also demonstrate its broader applicability. We release our source code at https://github.com/Ubisoft-LaForge/CompactPoissonFilters .

Compact Poisson Filters for Fast Fluid Simulation

Lingchen Yang, Byungsoo Kim, Gaspard Zoss, Baran Gözcü, Markus Gross, Barbara Solenthaler

Active soft bodies can affect their shape through an internal actuation mechanism that induces a deformation. Similar to recent work, this paper utilizes a differentiable, quasi-static, and physics-based simulation layer to optimize for actuation signals parameterized by neural networks. Our key contribution is a general and implicit formulation to control active soft bodies by defining a function that enables a continuous mapping from a spatial point in the material space to the actuation value. This property allows us to capture the signal’s dominant frequencies, making the method discretization agnostic and widely applicable. We extend our implicit model to mandible kinematics for the particular case of facial animation and show that we can reliably reproduce facial expressions captured with high-quality capture systems. We apply the method to volumetric soft bodies, human poses, and facial expressions, demonstrating artist-friendly properties, such as simple control over the latent space and resolution invariance at test time.

Implicit Neural Representation for Physics-driven Actuated Soft Bodies

Xuwen Chen, Xingyu Ni, Bo Zhu, Bin Wang, Baoquan Chen

Magnetoelastic thin shells exhibit great potential in realizing versatile functionalities through a broad range of combination of material stiffness, remnant magnetization intensity, and external magnetic stimuli. In this paper, we propose a novel computational method for forward simulation and inverse design of magnetoelastic thin shells. Our system consists of two key components of forward simulation and backward optimization. On the simulation side, we have developed a new continuum mechanics model based on the Kirchhoff–Love thin-shell model to characterize the behaviors of a megnetolelastic thin shell under external magnetic stimuli. Based on this model, we proposed an implicit numerical simulator facilitated by the magnetic energy Hessian to treat the elastic and magnetic stresses within a unified framework, which is versatile to incorporation with other thin shell models. On the optimization side, we have devised a new differentiable simulation framework equipped with an efficient adjoint formula to accommodate various PDE-constraint, inverse design problems of magnetoelastic thin-shell structures, in both static and dynamic settings. It also encompasses applications of magnetoelastic soft robots, functional Origami, artworks, and meta-material designs. We demonstrate the efficacy of our framework by designing and simulating a broad array of magnetoelastic thin-shell objects that manifest complicated interactions between magnetic fields, materials, and control policies.

Simulation and Optimization of Magnetoelastic Thin Shells